That isn’t the correct explanation.

First - To me "escape" means that you’re inside. Nothing from the inside can get outside. It’s not even possible for an outside observer to speak of things moving inside the hole. However a person could exist inside a blackhole if it was big enough. If he had a flashlight then no matter where he pointed it then light would eventually fall into the singularity.

Second - Time dialation and gravitational redshift is often explained incorrectly. Sometimes you’ll see that the light’s frequency changes as it gets closer to or further from the hole. This description in incomplete. One needs to state by whos clock the frrequency change is being measured. The answer is that no single observer will reckon a change in the light. Only the comparison of different observers results will yield a difference. For example: If I send pulses to an observer near the hole then I will reckon the pulses to get there at the same rate at which I sent them. Therefore the frequency of the light will also not change. However since the observer’s clock near the hole is running slower than mine he will deteccted a frequency larger than I sent. It is in this sense that time slows down near the event horizon.

Third - re "photon’s point of view" - Same as a person’s point of view if he could survive the plunge. A person could plunge through the event horixon and exist inside a blackhole if it the hole was big enough. If he had a flashlight then no matter where he pointed it the light would eventually fall into the singularity. It may even appear to him that the light is moving out but that is mere appearances.